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Rashba spin-orbit interaction leads to a number of electromagneticcross-correlation effects by inducing a mixing of electric and magnetic degreesof freedom. In this study, we investigate the optical properties of a magneticRashba conductor by deriving an effective Hamiltonian based on animaginary-time path-integral formalism. We show that the effective Hamiltoniancan be described in terms of toroidal and quadrupole moments, as has beenargued in the case of insulator multiferroics. The toroidal moment turns out tocoincide with the spin gauge field induced by the Rashba field. It causesDoppler shift by inducing intrinsic spin current, resulting in anisotropiclight propagation (directional dichroism) irrespective of the polarization. Thequadrupole moment on the other hand results in a magneto-optical phenomenonsuch as a Faraday effect for circularly-polarized waves.

Effective Hamiltonian theory for nonreciprocal light propagation in magnetic Rashba conductor